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<div class="section">
<div class="titlepage"><div><div>
<h2 class="title">
<a id="decay-functions"></a>The Closer, The Better<a class="edit_me edit_me_private" rel="nofollow" title="Editing on GitHub is available to Elastic" href="https://github.com/elastic/elasticsearch-definitive-guide/edit/2.x/170_Relevance/60_Decay_functions.asciidoc">edit</a>
</h2>
</div></div></div>
<p>Many variables could influence the user’s choice of vacation
home.  Maybe she would like to be close to the center of town, but perhaps
would be willing to settle for a place that is a bit farther from the
center if the price is low enough.  Perhaps the reverse is true: she would be
willing to pay more for the best location.</p>
<p>If we were to add a filter that excluded any vacation homes farther than 1
kilometer from the center, or any vacation homes that cost more than £100 a
night, we might exclude results that the user would consider to be a good
compromise.</p>
<p>The <code class="literal">function_score</code> query gives us the ability to trade off one sliding scale
(like location) against another sliding scale (like price), with a group of
functions known as the <em>decay functions</em>.</p>
<p>The three decay functions—​called <code class="literal">linear</code>, <code class="literal">exp</code>, and <code class="literal">gauss</code>—operate on numeric fields, date fields, or lat/lon geo-points.  All three take
the same parameters:</p>
<div class="variablelist">
<dl class="variablelist">
<dt>
<span class="term">
<code class="literal">origin</code>
</span>
</dt>
<dd>
The <em>central point</em>, or the best possible value for the field.
Documents that fall at the <code class="literal">origin</code> will get a full <code class="literal">_score</code> of <code class="literal">1.0</code>.
</dd>
<dt>
<span class="term">
<code class="literal">scale</code>
</span>
</dt>
<dd>
The rate of decay—​how quickly the <code class="literal">_score</code> should drop the further from
the <code class="literal">origin</code> that a document lies (for example, every £10 or every 100 meters).
</dd>
<dt>
<span class="term">
<code class="literal">decay</code>
</span>
</dt>
<dd>
The <code class="literal">_score</code> that a document at <code class="literal">scale</code> distance from the <code class="literal">origin</code> should
receive. Defaults to <code class="literal">0.5</code>.
</dd>
<dt>
<span class="term">
<code class="literal">offset</code>
</span>
</dt>
<dd>
Setting a nonzero <code class="literal">offset</code> expands the central point to cover a range
of values instead of just the single point specified by the <code class="literal">origin</code>. All
values in the range <code class="literal">-offset &lt;= origin &lt;= +offset</code> will receive the full
<code class="literal">_score</code> of <code class="literal">1.0</code>.
</dd>
</dl>
</div>
<p>The only difference between these three functions is the shape of the decay
curve. The difference is most easily illustrated with a graph (see <a class="xref" href="decay-functions.html#img-decay-functions" title="Decay function curves">Figure 33, “Decay function curves”</a>).</p>
<div id="img-decay-functions" class="imageblock">
<div class="content">
<img src="images/elas_1705.png" alt="The curves of the decay functions">
</div>
<div class="title">Figure 33. Decay function curves</div>
</div>
<p>The curves shown in <a class="xref" href="decay-functions.html#img-decay-functions" title="Decay function curves">Figure 33, “Decay function curves”</a> all have their <code class="literal">origin</code>—the
central point—​set to <code class="literal">40</code>.  The <code class="literal">offset</code> is <code class="literal">5</code>, meaning that all values in
the range <code class="literal">40 - 5 &lt;= value &lt;= 40 + 5</code> are treated as though they were at the
<code class="literal">origin</code>—they all get the full score of <code class="literal">1.0</code>.</p>
<p>Outside this range, the score starts to decay.  The rate of decay is
determined by the <code class="literal">scale</code> (which in this example is set to <code class="literal">5</code>), and the
<code class="literal">decay</code> (which is set to the default of <code class="literal">0.5</code>). The result is that all three
curves return a score of <code class="literal">0.5</code> at <code class="literal">origin +/- (offset + scale)</code>, or at points
<code class="literal">30</code> and <code class="literal">50</code>.</p>
<p>The difference between <code class="literal">linear</code>, <code class="literal">exp</code>, and <code class="literal">gauss</code> is the shape of the curve at other points in the range:</p>
<div class="ulist itemizedlist">
<ul class="itemizedlist">
<li class="listitem">
The <code class="literal">linear</code> funtion is just a straight line. Once the line hits zero,
all values outside the line will return a score of <code class="literal">0.0</code>.
</li>
<li class="listitem">
The <code class="literal">exp</code> (exponential) function decays rapidly, then slows down.
</li>
<li class="listitem">
The <code class="literal">gauss</code> (Gaussian) function is bell-shaped—​it decays slowly, then
rapidly, then slows down again.
</li>
</ul>
</div>
<p>Which curve you choose depends entirely on how quickly you want the <code class="literal">_score</code>
to decay, the further a value is from the <code class="literal">origin</code>.</p>
<p>To return to our example: our user would prefer to rent a vacation home close
to the center of London (<code class="literal">{ "lat": 51.50, "lon": 0.12}</code>) and to pay no more
than £100 a night, but our user considers price to be more important than
distance.   We could write this query as follows:</p>
<div class="pre_wrapper lang-json">
<pre class="programlisting prettyprint lang-json">GET /_search
{
  "query": {
    "function_score": {
      "functions": [
        {
          "gauss": {
            "location": { <a id="CO119-1"></a><i class="conum" data-value="1"></i>
              "origin": { "lat": 51.5, "lon": 0.12 },
              "offset": "2km",
              "scale":  "3km"
            }
          }
        },
        {
          "gauss": {
            "price": { <a id="CO119-2"></a><i class="conum" data-value="2"></i>
              "origin": "50", <a id="CO119-3"></a><i class="conum" data-value="3"></i>
              "offset": "50",
              "scale":  "20"
            }
          },
          "weight": 2 <a id="CO119-4"></a><i class="conum" data-value="4"></i>
        }
      ]
    }
  }
}</pre>
</div>
<div class="calloutlist">
<table border="0" summary="Callout list">
<tr>
<td align="left" valign="top" width="5%">
<p><a href="#CO119-1"><i class="conum" data-value="1"></i></a></p>
</td>
<td align="left" valign="top">
<p>The <code class="literal">location</code> field is mapped as a <code class="literal">geo_point</code>.</p>
</td>
</tr>
<tr>
<td align="left" valign="top" width="5%">
<p><a href="#CO119-2"><i class="conum" data-value="2"></i></a></p>
</td>
<td align="left" valign="top">
<p>The <code class="literal">price</code> field is numeric.</p>
</td>
</tr>
<tr>
<td align="left" valign="top" width="5%">
<p><a href="#CO119-3"><i class="conum" data-value="3"></i></a></p>
</td>
<td align="left" valign="top">
<p>See <a class="xref" href="Understanding-the-price-Clause.html" title="Understanding the price Clause">Understanding the price Clause</a> for the reason that <code class="literal">origin</code> is <code class="literal">50</code> instead of <code class="literal">100</code>.</p>
</td>
</tr>
<tr>
<td align="left" valign="top" width="5%">
<p><a href="#CO119-4"><i class="conum" data-value="4"></i></a></p>
</td>
<td align="left" valign="top">
<p>The <code class="literal">price</code> clause has twice the weight of the <code class="literal">location</code> clause.</p>
</td>
</tr>
</table>
</div>
<p>The <code class="literal">location</code> clause is easy to understand:</p>
<div class="ulist itemizedlist">
<ul class="itemizedlist">
<li class="listitem">
We have specified an <code class="literal">origin</code> that corresponds to the center of London.
</li>
<li class="listitem">
Any location within <code class="literal">2km</code> of the <code class="literal">origin</code> receives the full score of <code class="literal">1.0</code>.
</li>
<li class="listitem">
Locations <code class="literal">5km</code> (<code class="literal">offset + scale</code>) from the centre receive a score
of <code class="literal">0.5</code>.
</li>
</ul>
</div>
</div>
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